In 2012 and 2013 we discovered a form of x-ray white-light interferometry, and based on it a type of x-ray phase contrast imaging method capable of detecting the refractive bending of x-rays at sub-nanoradian resolution with broadband x-ray sources. We invented a way to retrieve the phase information without the need for mechanical scanning, and an adaptive image reconstruction algorithm to suit future application environments outside the ideal laboratory setting. These methods are further developed and optimized, on the path towards realizing the benefit x-ray phase-contrast imaging in clinical applications. In 2014 we discovered a wave phenomenon which we named the phase moire effect. This effect allowed us to realize x-ray white-light interferometry in a benchtop system with conventional x-ray tubes. The benchtop system is called a polychromatic far-field interferometer (PFI). In collaboration with Dr. Priya Bhandarkar of Walter Reed NMMC we demonstrated its extraordinary sensitivity at low radiation dose levels compared to a clinical mammography scan. We also gained a thorough understanding of the physical mechanism through comprehensive theoretical and numerical analysis and comparison with experimental measurements. This understanding helps with future designs of new imaging methods. The central hardware necessary for the new imaging method is hard x-ray diffraction gratings of 200 nm periods. They are developed in another project of our laboratory in collaboration with NIST.